Plan on swapping to Miche Pista Advanced Track Crankset, Miche Primato ISO Taper BB and a different COG and chain on my '09 Capo (setup as fixed).

What specality tools and lubes are needed to do this? Never done this before. I have basic tools (rubber mallet, hex wrenches, wrenches, sockets, etc.) but nothing specifically for bikes. I assume I will need some grease for the BB too, but not sure which kind.

crank puller
bottom bracket tool
lockring wrench/spanner
chainwhip or just rotafix it

This is the bottom bracket tool that you will need. I just did that exact swap on my Capo. Hit me up with any specific questions. The bolts on the stock cranks were a mother to get loose. Get some blue threadlocker for the bb cups too.

https://www.pedros.com/products_tools.htm (It's the Campy one)

Excellent! Thanks both of you! If I have any other questions i'll be sure to ask.

https://bicycletutor.com/replace-cotterless-cranks/
https://bicycletutor.com/cartridge-bottom-bracket/

why do you capitalize the word cog?

I have and highly recommend both of these: Shimano SR-22 lockring spanner/1/8 chainwhip and Park CCP-4 crank puller

The Shimano tool is actually a good deal even though it's $40+ because it works much better than a cheap lockring tool and a cheap chainwhip, which will be $20 each anyway.

Ummmmm, no idea

Those tools look good. Should I use that waterproof marine grease for installing everything?